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## The Physics of Hadrons

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**The Physics of Hadrons**Craig D. RobertsPhysics DivisionArgonne National Laboratory & School of PhysicsPeking University**Length-Scales of Physics**Craig Roberts, Physics Division: The Physics of Hadrons**Hadron Physics**“Hadron physics is unique at the cutting edge of modern science because Nature has provided us with just one instance of a fundamental strongly-interacting theory; i.e., Quantum Chromodynamics (QCD). The community of science has never before confronted such a challenge as solving this theory.” Craig Roberts, Physics Division: The Physics of Hadrons**Nuclear Science Advisory CommitteeLong Range Plan**Craig Roberts, Physics Division: The Physics of Hadrons “A central goal of (DOE Office of) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD.”**What is QCD?**• Relativistic Quantum Gauge Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless • Similar interaction in QED • Special feature of QCD – gluon self-interactions, which completely change the character of the theory 3-gluon vertex 4-gluon vertex Craig Roberts, Physics Division: The Physics of Hadrons**QED cf. QCD?**5 x10-5 Add 3-gluon self-interaction gluon antiscreening fermion screening Craig Roberts, Physics Division: The Physics of Hadrons • 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek**Quarks and Nuclear Physics**• Standard Model of Particle Physics: • Six quark flavours • Real World • Normal matter – only two • light-quark flavours are active • Or, perhaps, three • For numerous good reasons, • much research also focuses on • accessible heavy-quarks • Nevertheless, I will focus on • the light-quarks; i.e., u & d. Craig Roberts, Physics Division: The Physics of Hadrons**Ford Nucleon, 1958atomic powered car**Two Key Hadronsnucleon = neutron & proton Craig Roberts, Physics Division: The Physics of Hadrons • Fermions – two static properties: proton electric charge = +1; and magnetic moment, μp • Magnetic Moment discovered by Stern & collaborators -1933; Awarded Nobel Prize in 1943 Dirac (1928) – pointlikefermion: μp = e/[2 M] • Stern (1933) – μp = (1 + 1.79) e/[2 M] Big Hint that Proton is not a point particle Proton has constituents These are Quarks and Gluons Quark discovery via e− p-scattering at SLAC in 1968 – the elementary quanta of Quantum Chromo-dynamics**Hadronstructure exposedvia studies of form factors**Point particle (Dirac): F2=0, hence μpGE=GM Craig Roberts, Physics Division: The Physics of Hadrons • Electron is an excellent probe because it’s structureless relativistic current: • Nucleon’s relativistic current**Distribution of charge and magnetisation is identical**Pre-2000μpGE/GM Strong support for simple s-wave models of nucleon structure Craig Roberts, Physics Division: The Physics of Hadrons**Simple picture- Proton**Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange Craig Roberts, Physics Division: The Physics of Hadrons**Simple picture- Pion**Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange Craig Roberts, Physics Division: The Physics of Hadrons**Thomas Jefferson National Accelerator Facility (JLAB)**Racecourse Accelerator Underground target halls Newport News, Virginia • 1994 – JLab begins operation • 1995 – Reaches design energy of 4GeV e– beams • 2000 – Reaches energy of 6GeV e– beams • 2009 – Construction begins on 12GeV upgrade • Annual budget in excess of $200-million • Upgrade is $310-million project Craig Roberts, Physics Division: The Physics of Hadrons**Data from JLab,**using new method allowed by high-luminosity, changes picture completely After-2000μpGE/GM Two puzzles: Reconcile the data If JLab correct, explain Charge distribution is markedly differtent from magnetisation distribution. Strong indication that nucleon has complicated internal structure. Craig Roberts, Physics Division: The Physics of Hadrons**Modern Miraclesin Hadron Physics**Craig Roberts, Physics Division: The Physics of Hadrons • proton = three constituent quarks • Mproton ≈ 1GeV • Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV • pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton≈ 700MeV • WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeV • Rho-meson • Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped • Mrho ≈ 770MeV ≈ 2 × Mconstituent−quark What is “wrong” with the pion?**Dichotomy of the pion**Craig Roberts, Physics Division: The Physics of Hadrons • How does one make an almost massless particle from two massive constituent-quarks? • Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless – but some are still making this mistake • However: current-algebra (1968) • This is impossible in quantum mechanics, for which one always finds:**NSACLong Range Plan?**• What is a constituent quark, a constituent-gluon? • Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Craig Roberts, Physics Division: The Physics of Hadrons • If not, with what should they be replaced? • What is the meaning of the NSAC Challenge?**What is themeaning of all this?**If mπ=mρ, then Repulsive & attractiveforces in the Nucleon-Nucleon potential have the SAME range … and … There is NO intermediate range attraction. Craig Roberts, Physics Division: The Physics of Hadrons Under these circumstances: • Can 12C be stable? • Is the deuteron stable; can Big-Bang Nucleosynthesis occur? (Many more existential questions …) Probably not … but it wouldn’t matter because we wouldn’t be around to worry about it.**QCD’s Challenges**Understand emergent phenomena • Quark and Gluon Confinement • No matter how hard one strikes the proton, • one cannot liberate an individual quark or gluon Craig Roberts, Physics Division: The Physics of Hadrons • Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners) • Neither of these phenomena is apparent in QCD’s LagrangianYetthey are the dominant determiningcharacteristics of real-world QCD. • QCD – Complex behaviour arises from apparently simple rules.**Why don’t we juststop talking & solve the problem?**Craig Roberts, Physics Division: The Physics of Hadrons • Emergent phenomena can’t be studied using perturbation theory • So what? Same is true of bound-state problems in quantum mechanics! • Differences: • Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field Theory • Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume! • Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory**Universal Truths**Craig Roberts, Physics Division: The Physics of Hadrons • Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron'scharacterising properties amongst its QCD constituents. • Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is (almost) irrelevant to light-quarks. • Running of quark mass entails that calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. • Confinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB.**Chiral symmetry**Craig Roberts, Physics Division: Much Ado About Nothing • Feature of massless fermions in relativistic quantum field theory • Realised in the spectrum of the theory via the appearance of degenerate parity partners • Perturbative QCD: u- & d- quarks are very light mu /md≈ 0.5 & md≈ 4MeV H. Leutwyler, 0911.1416 [hep-ph] • However, splitting between parity partners is greater-than 100-times this mass-scale; e.g.,**Universal Conventions**Craig Roberts, Physics Division: The Physics of Hadrons • Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”**Universal Misapprehensions**“The biggest embarrassment in theoretical physics.” Craig Roberts, Physics Division: The Physics of Hadrons • Since 1979, DCSB has commonly been associated literally with a spacetime-independent mass-dimension-three “vacuum condensate.” • Under this assumption, “condensates” couple directly to gravity in general relativity and make an enormous contribution to the cosmological constant • Experimentally, the answer is Ωcosm. const. = 0.76 • This mismatch is a bit of a problem.**How can we tackle the SM’sStrongly-interacting piece?**Craig Roberts, Physics Division: The Physics of Hadrons The Traditional Approach – Modelling – has its problems.**How can we tackle the SM’sStrongly-interacting piece?**– Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Craig Roberts, Physics Division: The Physics of Hadrons Lattice-QCD**How can we tackle the SM’sStrongly-interacting piece?**– Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & 20-30 people per collaboration. Craig Roberts, Physics Division: The Physics of Hadrons Lattice-QCD –**A Compromise?Dyson-Schwinger Equations**Craig Roberts, Physics Division: The Physics of Hadrons • 1994 . . . “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD]. . . . .”**A Compromise?Dyson-Schwinger Equations**Craig Roberts, Physics Division: The Physics of Hadrons • 1994 . . . “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework. . . . ”**A Compromise?Dyson-Schwinger Equations**Craig Roberts, Physics Division: The Physics of Hadrons • 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”**A Compromise?Dyson-Schwinger Equations**Craig Roberts, Physics Division: The Physics of Hadrons • 1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.” • C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224]. (473 citations)**A Compromise?DSEs**• Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. • Gap equation: • fermion self energy • gauge-boson propagator • fermion-gauge-boson vertex • These are nonperturbative equivalents in quantum field theory to the Lagrange equations of motion. • Essential in simplifying the general proof of renormalisability of gauge field theories. Craig Roberts, Physics Division: The Physics of Hadrons**Dyson-SchwingerEquations**• Approach yields • Schwinger functions; i.e., • propagators and vertices • Cross-Sections built from • Schwinger Functions • Hence, method connects • observables with long- • range behaviour of the • running coupling • Experiment ↔ Theory • comparison leads to an • understanding of long- • range behaviour of • strong running-coupling Craig Roberts, Physics Division: The Physics of Hadrons • Well suited to Relativistic Quantum Field Theory • Simplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model-Dependence … Statement about long-range behaviour of quark-quark interaction • NonPerturbative, Continuum approach to QCD • Hadrons as Composites of Quarks and Gluons • Qualitative and Quantitative Importance of: • Dynamical Chiral Symmetry Breaking – Generation of fermion mass from nothing • Quark & Gluon Confinement – Coloured objects not detected, Not detectable?**Mass from Nothing?!Perturbation Theory**Craig Roberts, Physics Division: The Physics of Hadrons • QCD is asymptotically-free (2004 Nobel Prize) • Chiral-limit is well-defined; i.e., one can truly speak of a massless quark. • NB. This is nonperturbativelyimpossible in QED. • Dressed-quark propagator: • Weak coupling expansion of gap equation yields every diagram in perturbation theory • In perturbation theory: If m=0, then M(p2)=0 Start with no mass, Always have no mass.**Spontaneous(Dynamical)Chiral Symmetry Breaking**Craig Roberts, Physics Division: The Physics of Hadrons The 2008Nobel Prize in Physics was divided, one half awarded to YoichiroNambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"**Gell-Mann – Oakes – RennerRelation (1968)**Craig Roberts, Physics Division: The Physics of Hadrons • Pion’sleptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν • Vacuum quark condensate How is this expression modified and interpreted in a theory with confinement?**Frontiers of Nuclear Science:Theoretical Advances**Craig Roberts, Physics Division: The Physics of Hadrons In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.**Frontiers of Nuclear Science:Theoretical Advances**Mass from nothing! DSE prediction of DCSB confirmed Craig Roberts, Physics Division: The Physics of Hadrons In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.**Frontiers of Nuclear Science:Theoretical Advances**Hint of lattice-QCD support for DSE prediction of violation of reflection positivity Craig Roberts, Physics Division: The Physics of Hadrons In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.**12GeVThe Future of JLab**Jlab 12GeV: Scanned by 2<Q2<9 GeV2 elastic & transition form factors. Craig Roberts, Physics Division: The Physics of Hadrons Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.**Universal Conventions**What does this approach tell us? ? Craig Roberts, Physics Division: The Physics of Hadrons • Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”**P. Maris, C.D. Roberts & P.C. Tandynucl-th/9707003**Dichotomy of the pion This is an almost-familiar relation, a peculiar, non-quantum-mechanical Identity – looks like the GMOR What are the constants of proportionality, physically? Craig Roberts, Physics Division: The Physics of Hadrons • Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD. • One of them explains the peculiar nature of the pion’s mass; i.e., it’s relationship to the Lagrangian current-quark mass m(ς):**In-meson condensate**Maris & Roberts nucl-th/9708029 Craig Roberts, Physics Division: The Physics of Hadrons • Pseudoscalar projection of pion’s Bethe-Salpeter wave-function onto the origin in configuration space: |ΨπPS(0)| – or the pseudoscalarpion-to-vacuum matrix element • Rigorously defined in QCD – gauge-independent, cutoff-independent, etc. • For arbitrary current-quark masses • For any pseudoscalar meson**In-meson condensate**Maris & Roberts nucl-th/9708029 Craig Roberts, Physics Division: The Physics of Hadrons • Pseudovector projection of pion’s Bethe-Salpeter wave-function onto the origin in configuration space:|ΨπAV(0)| – or the pseudoscalarpion-to-vacuum matrix element – or the pion’sleptonic decay constant • Rigorously defined in QCD – gauge-independent, cutoff-independent, etc. • For arbitrary current-quark masses • For any pseudoscalar meson**In-meson condensate**Maris & Roberts nucl-th/9708029 Chiral limit |ΨπPS(0)|*|ΨπAV(0)| Craig Roberts, Physics Division: The Physics of Hadrons • Define • Then, using the pion Goldberger-Treiman relations, one derives, in the chiral limit • Namely, the so-called vacuum quark condensate is the chiral-limit valueof the in-pion condensate • The in-pion condensate is the only well-defined function of current-quark mass in QCD that is smoothly connected to the vacuum quark condensate.**Nature of the Pion:QCD’s Goldstone Mode**Craig Roberts, Physics Division: The Physics of Hadrons**Nature of the Pion:QCD’s Goldstone Mode**2 → many or infinitely many Nature and number of constituents depends on the wavelength of the probe Constituent- quarks are replaced by the dressed-quarks and –gluons of QCD Craig Roberts, Physics Division: The Physics of Hadrons**Paradigm shift:In-Hadron Condensates**Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS QCD Craig Roberts, Physics Division: The Physics of Hadrons • Resolution • Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. • So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. • GMOR cf.**Paradigm shift:In-Hadron Condensates**Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS And |π> →|0> matrix elements Craig Roberts, Physics Division: The Physics of Hadrons • Resolution • Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. • So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. • No qualitative difference betweenfπand ρπ • Both are equivalent order parameters for DCSB**Paradigm shift:In-Hadron Condensates**Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS Chiral limit ONLY expression related to the condensate that is rigorously defined in QCD for nonzero current-quark mass Craig Roberts, Physics Division: The Physics of Hadrons • Resolution • Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. • So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. • No qualitative difference between fπand ρπ • And